Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
A. Gupta , Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC, Canada
The proof of Wagner's conjecture by N. Robertson and P. Seymour gives a finite description of any family of graphs which is closed under the minor ordering, called the obstructions of the family. Since the intersection and the union of two minor closed graph families are again a minor closed graph family, an interesting question is that of computing the obstructions of the new family given the obstructions for the original two families. It is easy to compute the obstructions of the intersection, but, until very recently, it was an open problem to compute the obstructions of the union. It is shown that if the original families are planar, then the obstructions of the union are no larger than n to the O(n/sup 2/) power, where n is the size of the largest obstruction of the original family.
minor closed graph families, graph family obstructions, planar intertwines, minor ordering
R. Impagliazzo and A. Gupta, "Computing planar intertwines,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 802-811.